Problem9392--ABC205 —— D - Kth Excluded

9392: ABC205 —— D - Kth Excluded

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

You are given a sequence of $N$ positive integers: $A = (A_1, A_2, \dots, A_N)$, and $Q$ queries.

In the $i$-th query $(1 \leq i \leq Q)$, given a positive integer $K_i$, find the $K_i$-th smallest integer among the positive integers that differ from all of $A_1, A_2, \dots, A_N$.

Input

Input is given from Standard Input in the following format:

```
$N$ $Q$
$A_1$ $A_2$ $\ldots$ $A_N$
$K_1$
$K_2$
$\vdots$
$K_Q$
```

Output

Print $Q$ lines. The $i$-th line should contain the response to the $i$-th query.

Constraints

-   $1 \leq N, Q \leq 10^5$
-   $1 \leq A_1 < A_2 < \dots < A_N \leq 10^{18}$
-   $1 \leq K_i \leq 10^{18}$
-   All values in input are integers.

Sample 1 Input

4 3
3 5 6 7
2
5
3

Sample 1 Output

2
9
4
The positive integers that differ from all of $A_1,A_2,…,A_N$ are 1,2,4,8,9,10,11,… in ascending order. The second, fifth, and third smallest of them are 2, 9, and 4, respectively.

Sample 2 Input

5 2
1 2 3 4 5
1
10

Sample 2 Output

6
15

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